1. Field of the Invention
The present invention relates to transmission electron microscopy and more specifically, it relates to the use of a modified transmission electron microscope to image magnetic properties quantitatively.
2. Description of Related Art
Various modes of Lorentz transmission electron microscopy provide high resolution (5-100 nm) together with high sensitivity to the local variation of magnetic induction. The image contrast is a result of the deflection experienced by the electron beam when it interacts with the magnetic induction of the specimen. The most commonly used modes are Foucault and Fresnel imaging. In the Foucault mode an opaque aperture in the back-focal plane selectively stops the electrons deflected in certain orientation corresponding to particular oriented magnetic domains. Those areas appear dark in the image. In the Fresnel mode the domain walls are revealed as narrow light and dark areas when the specimen is out of focus. Both methods are rather easy to implement and are suitable to select a region of interest to be studied by the new quantitative phase-contrast imaging technique described here.
However, the images obtained with the above mentioned methods are only qualitative. Differential phase contrast imaging and a known method of coherent Foucault imaging provide a more quantitative description of the induction variation but they require a highly coherent source. But none of these methods gives absolute values of the magnetic induction.
The only other method to the one that we are describing in this document, that can give the absolute value of the phase and therefore the magnetic induction or magnetization, is the electron holography method. However, this method also requires a highly coherent source (which is extremely expensive), it is technically complicated to do and the reconstruction of the electron holograms requires lots of time and effort.
It is an object of the present invention to provide a method for measuring magnetic properties quantitatively.
The magnetic microscopy method of the present invention can be used to improve the theoretical models that calculate the magnetic response from first principles by comparing the theoretical calculations and the experimental results to obtain quantitative images.
Quantitative imaging is of interest to the magnetic recording and storage industry to study the magnetic properties of very small structures and correlate them with their crystalline microstructure. The present microscope would enable that industry to understand what is happening on a nano-meter scale and to develop better magnetic storage media and magnetic sensors.
The present invention uses a non-interferometric phase contrast imaging technique and applies it to image magnetic domains using electrons. The non-interferometric phase contrast imaging technique using a transmission electron microscope and imaging thin magnetic structures gives absolute phase information but it is desirable to extract the magnetization vector distribution in a magnetic structure. To obtain the magnetization vector distribution, one needs first to calculate the gradient of the phase. The gradient of the phase is proportional to the magnetic induction (B). So, once you have the gradient of the phase, the Lorentz force may be obtained and finally the magnetization vector. The Lorentz force is connected with the magnetic induction (B) by the equation:
F=e(vxc3x97B),
where e represents the electric charge of the electron, v is the velocity vector of the electron and B is the magnetic induction vector in the material. The magnetization vector can be derived from the following formula:
M=(Bxe2x88x92H0)/4xc2x7.
If the external applied magnetic field (H0) is zero then the magnetization vector is directly proportional to the magnetic induction, otherwise the external magnetic field has to be subtracted.
A description of how to obtain the absolute phase using non-interferometric phase contrast imaging follows. To obtain information about the phase using non-interferometric measurement, one needs to consider that if the electron beam is monochromatic and paraxial, the wave equation can be written in a form called the transport-of-intensity equation. This relates three quantities: the intensity in the plane, the intensity derivative normal to the plane and the phase in the plane. Both the intensity and the intensity derivative can be measured directly. The phase can be calculated from the transport-of-intensity equation as described in Paganin and Nugent""s paper (Paganin D., Nugent K. A., 1998, Phys. Rev. Lett. 80, 2586) incorporated herein by reference. The algorithm is deterministic and yields a unique solution, provided that there are no dislocations in the phase front. Two intensity measurements in closely spaced planes are needed to determine the phase front. The measurement in focus gives the intensity and the difference between the intensities in focus and out of focus gives the intensity derivative. The intensity derivative contains the information about the phase of the wave in the plane. If, for example, the phase front of the wave has locally some curvature then the electrons will get slightly focused or defocused as they travel from one plane to the other. Therefore the intensity derivative is a measure of the wavefront curvature. The wavefront curvature is a function of both the intensity and the phase of the wave and is proportional to the intensity derivative, as shown in the Paganin and Nugent""s paper, as cited above The transport-of-intensity equation gives the intensity derivative as a function of the intensity and the phase. The solution gives the phase as a function of the intensity and the intensity derivative.
The gradient of the phase is proportional to the magnetic induction. The magnetic induction is a sum of the magnetization and the external magnetic field. All the above quantities are vectors, so in additioning to obtain their absolute values, the direction is also extracted. Vector maps, showing the direction and the magnitude of magnetization can be produced. FIG. 1 shows the recovered phase image of cobalt grain. The figure is a greyscale image of the phase structure, which is also represented as a surface plot in FIG. 1B. FIG. 1C shows magnetism extracted from the phase image of FIG. 1A.
To do the experiment one needs a TEM microscope. It is important that this method does not require a highly coherent source because this means it can be easily applied to an older TEM microscope. It is beneficial to set the TEM microscope up to perform the imaging in almost zero magnetic field so that the original magnetic microstructure remains unchanged during the experiment.
In addition it is also possible to observe the dynamic effects by applying a controlled external magnetic field on the specimen or to study the thermal effects by heating the specimen in-situ. The images are recorded digitally with CCD camera with large dynamic range. The usual data file consists of (1024xc3x971024)xc3x9716 bits. Specimens have been deposited directly on a thin silicon nitride membrane to avoid any extra sample preparation. The samples imaged were cobalt structures ranging from 10 to 50 nm in thickness. The monochromatic electrons used in the experiments had an energy of 200 keV (wavelength=2.5xc3x9710xe2x88x9212 m) although some experiments were performed using electrons with lower energies. The use of higher energy electrons is preferable because they give a higher spatial resolution. Using 200 keV electrons and the modification described above improved the spatial resolution to about 10 nm. The TEM samples have to be transparent to the electron beam to get an image of the specimen, but the maximum thickness allowed is a strong function of the density of the specimen and of the energy of the electrons. Co structures were able to be imaged that were 100 nm thick and deposited on 40 nm silicon nitride membranes. In order to do the calculations two to three images taken under the same experimental conditions of the same specimen are needed. The images have to be taken as close in time to each other as possible to minimize the drift in the image. A computer code may be used to correct for such drift. Usually an image in focus, one over-focused and one under-focused are taken. Steps of 0.23xc2x7m seem to give good results for the 200 keV electrons. In addition to the digital images the parameters needed to perform the calculation are the wavelength of the electrons, the thickness of the structure, the image size and the defocus value. It usually takes only few seconds to record one image and few seconds of computer time to do the calculations to obtain the quantitative phase contrast images.
The above mentioned TEM modification does not interfere with the conventional TEM mode. Actually, the specimen is usually placed high above the objective to do quantitative phase contrast imaging and then just above the objective lens to do the conventional microscopy, such as to study the micro-crystallinity, the micro-diffraction and micro-composition. The spatial resolution when imaging magnetic domains is around 10 nm. This spatial resolution is limited only by the spatial resolution of the TEM under those conditions. This means that much higher spatial resolution could be achieved on a newer TEM microscope.
When a wavefield is incident on a sample both its intensity and its phase are modified. For many samples of interest in the electron microscopy of biological samples and of materials, the modulation of the intensity of the wave can be negligibly small, whereas the impact on the phase may be quite strong. There is therefore a great deal of interest in the imaging of phase in electron microscopy.
A number of techniques have been evolved that allow the phase to be rendered visible, including Zernike phase contrast and Foucault imaging. However, neither of these techniques allows the phase to be determined quantitatively. For the phase to be measured, electron holography may be used. This technique requires a highly coherent electron source and so is not possible using a conventional transmission electron microscope.